Question

In frame S, a particle passes through the origin at time t=0 with a constant velocity U=5m/s making an angle €=tan-1(3/4) with x-axis. Find the position of the particle at time t=2s.Assume another frame S’ which is moving relative to S with velocity V=1m/s x. Find the speed of the particle and its location at time t=2s in frame S’

Answer 1

The angle of the velocity relative to the x-axis is atan(3/4). Therefore, in 2 seconds, the x-coordinate of the particle will be

$$x_2^S=v\text{ cos}\bigg(\text{atan}\frac{3}{4}\bigg)t=8\text{ m}.$$

If the frame S' moves with a speed of 1 m/s along the x-axis of S to the right, the x-coordinate will be

$$x_2^{S'}=\bigg[v\text{ cos}\bigg(\text{atan}\frac{3}{4}\bigg)-u\bigg]t=6\text{ m}.$$